I'm honestly not sure if 4.3.4 works with Joomla 2.5.19. At the time of 4.3.4's release (in January 2013), the latest release of Joomla was 2.5.8. There have been many changes in Joomla since then, though none that I know of that would have broken compatibility with JFBConnect v4.3.4.
Unfortunately, we simply don't test with releases that are more than a year old. The most recent version of JFBConnect is 6.0.4, which is 2 major versions beyond the release you're trying to use. That definitely works with 2.5.19 as we test the most recent releases for compatibility with each new Joomla release.
Sorry I can't be more specific as to compatibility. JFBConnect has many releases to keep up compatibility with both Joomla and the social networks we integrate with. Both change frequently, so it's always recommended to be using the latest releases.
I hope that helps,
Alex